Rectangleville's limits form a perfectly rectangular shape whose length is $20$ kilometers and width is $12$ kilometers. It has a population density of $320$ people per square kilometer. What is the population of Rectangleville? Round your answer, if necessary, to the nearest integer.
This is a density word problem. To solve it, we can use the following equation, which is the area definition of density: ${\text{Density}}=\dfrac{{\text{Total quantity}}}{{\text{Area}}}$ What do we know? Rectangleville's length is $20$ kilometers and its width is $12$ kilometers (we can use this to find the ${\text{area}}$ ). The population ${\text{density}}$ is ${320}$ people per square kilometer. What do we need to find? Rectangleville's population. This is the ${\text{total quantity}}$. The ${\text{area}}$ is $20\cdot 12={240}$ square kilometers. Let's denote the total population as $ n$. Now we can plug ${\text{density}=320}$, ${\text{total quantity}=n}$, and ${\text{area}=240}$ in the equation. $\begin{aligned} {\text{Density}}&=\dfrac{{\text{Total quantity}}}{{\text{Area}}} \\\\ {320}&=\dfrac{{n}}{{240}} \\\\ {240}\cdot{320}&=\dfrac{{n}}{\cancel{{240}}}\cdot\cancel{{240}} \\\\ 76{,}800&= n \end{aligned}$ Rectangleville's population is $76{,}800$ people.